Arsenal boss Arsene Wenger has warned Edu to sign a new contract or risk spending five months on the sidelines.
Wenger may dip into the transfer market if the Brazilian midfielder, 26, fails to sign a new deal by January.
The Gunners boss said: "There is an offer from us but if he doesn't take up our offer we have to consider the situation is not in our hands.
"He can sign elsewhere on 2 January, and it would be difficult to be completely committed to this club."
Sylvain Wiltord found to his cost last season that Wenger does not mince his words.
Wiltord failed to agree on a new deal and was cold-shouldered for the last few months of his time at Highbury.
Edu is said to be concerned about his chances of a regular first-team place after the emergence this season of teenager Cesc Fabregas.
His involvement with the Brazil squad has also caused problems, with the midfielder missing the start of this season to play in a friendly.
Edu has been linked with a move to Barcelona and if he fails to sign a new contract with Arsenal, he can start negotiating with overseas clubs on 1 January.
Wenger said: "He has an offer from us that shows we want to keep him. But I
can accept it if that isn't good enough and he feels he can get more somewhere
else.
"I'm not surprised as he's a great player. He's a professional footballer
and, if he can get a better offer, then he has to consider that.
"But we must consider what is in the best interests of the club. We have a
wage scale here that must be respected.
"We would buy someone experienced who would be available straight away as we
already have Cesc Fabregas and Mathieu Flamini."
Wenger, who insists he wants Edu to stay, has reminded the player of his situation when he arrived at Highbury.
"I want him to stay as I got him when he was completely unknown," said Wenger.
"He has made a big name for himself and become a Brazilian national player.
"He also had a passport problem, when we had to wait for six months. But I understand and respect his position."